Question

calcule senx, cosx, tgx nas figuras abaixo: ​

Answer 1

Resposta:

Teorema de Pitágoras:

${a}^{2} = {b}^{2} + {c}^{2} \\ \\ {10}^{2} = {4}^{2} + {c}^{2} \\ \\ {c}^{2} = {10}^{2} - {4}^{2} \\ \\ {c}^{2} = 100 - 16 \\ \\ {c}^{2} = 84 \\ \\ c = \sqrt{84} \\ \\ c = \sqrt{4 \times 21} \\ \\ c = \sqrt{4} \times \sqrt{21} \\ \\ \pink{c = 2 \sqrt{21} }$

$\sin(x) = \dfrac{2 \sqrt{21} \div 2}{10 \div 2} \\ \\ \green{sin(x) = \dfrac{ \sqrt{21} }{5} }$

$\cos(x) = \dfrac{4 \div 2}{10 \div 2} \\ \\ \green{\cos(x) = \dfrac{2}{5} }$

$\tan(x) = \dfrac{ \dfrac{ \sqrt{21} }{5} }{ \dfrac{2}{5} } \\ \\ \tan(x) = \dfrac{ \sqrt{21} }{ \red5} \times \dfrac{ \red5}{2} \\ \\ \green{\tan(x) = \dfrac{ \sqrt{21} }{2} }$

Bons Estudos!